College Physics Problem. Please show all work. Astronomical observations of our

Question

College Physics Problem. Please show all work.

Astronomical observations of our Milky Way galaxy indicate that it has a mass of about 8. x 101 solar masses. A star mass is concentrated near its center.) (a) What should the orbital period of that star be? yr (b) If its period is 6.0 x 107 years instead, what is the mass of the galaxy? Such calculations are used to imply the existence of "dark matter" in the universe and have indicated, for example, the existence of very massive black holes at the centers of some galaxies. solar masses

Explanation / Answer

a) We know that

T = sqrt (4*pi2*r3 / GM), Notice we have to get r in seconds, we are given r in light years

Putting in all the given values and constants as well, we have

T = sqrt (4*pi2*5.3016e203 / 6.67e-11*8e11*1.99e30)

T = 7.44329e15 seconds

In years, T = 2.358e8 years

b) Using the same formula, we now need to solve for M

   T = sqrt (4*pi2*r3 / GM)

SO, in terms of M , we have

M = 4*pi2*r3 / GT2

M = 4*pi2*5.3016e203 / 6.67E-11*(1.89345E15)2

Solve it, and divide the answer by 1.99e30 to get the answer in terms of solar masses.

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